Conic D-branes

The shape of D-branes is of fundamental interest in string theory. We find that generically D-branes in trivial spacetime can form a conic shape under external uniform forces. Surprisingly, the apex angle is found to be unique, once the spatial dimensions of the cone is given. In particular it is universal irrespective of the external forces. The quantized angle is reminiscent of Taylor cones of hydrodynamic electrospray. We provide explicit D-brane solutions as well as the mechanism of a force balance on the cone, for D-branes in RR and NSNS flux backgrounds. Critical embedding of probe D-branes in AdS/CFT with electric and magnetic fields is in the same category, for which we give an analytic proof of a power-low spectrum of "turbulent meson condensation."